Indeed, several TNG episodes mention that the E-D has to pay a price for her repeated use of highest possible speeds: the expectation would be that a ship of this class would not need the sort of maintenance she gets in, say, "Phantasms".

So there isn't such a thing as "impossible speed" vs. "possible speed". There are just different levels of risk to be taken. Sit on the safety valve, and even Kirk's old rust bucket will reach Ludicrous Speed. Moments before she blows up, that is.